How to unwrap multiple planes and have them exactly overlap?
You can do this by using magic UV addon. 

After enable addon go to edit mode, select one plane, unwrap it how you need, than press U -> copy/paste UV -> Copy UV

Next select all planes with same size and U -> copy/paste UV -> Paste UV 

In this case you need to repeat this operation as many times as you have variations in length.

UPD Found this addon: Textools that can easily achieve your task: